Systems for debiting a subscriber participating in a toll call are known, for example, from commonly owned U.S. Pat. Nos. 3,591,723 and 3,657,482 granted to Giorgio Dal Monte. These systems, however, relate to exchanges of the space-division type, i.e. wherein the several subscriber lines (or their extensions terminating at the exchange) are physically separated and individually accessible through cross-bar switches or the like. Such debiting systems are not readily adaptable to the TDM exchanges in which simultaneous connections between different subscriber pairs are established in respective time slots of a communication frame recurring, for example, 8000 times per second so as to have a duration of 125 .mu.s. This type of TDM exchange has been described in commonly owned U.S. Pat. No. 3,581,016 granted to Saverio Martinelli and Giorgio De Varda. Such an exchange comprises a group of synchronously circulating memories for the temporary storage of data relating to the progress of the several connections concurrently established, the operating cycle of these memories coinciding with a communication frame and being subdivided into a multiplicity of phases (e.g. 100) corresponding to the time slots of that frame. More specifically, the group comprises a caller memory registering in its phases the addresses (i.e. call numbers) or respective calling parties, a responder memory registering in corresponding phases the addresses of respective called parties, and a monitoring memory whose corresponding phases contain entries which identify successive stages in the establishment and consummation of a connection. More particularly, the entries in the phases of the monitoring memory according to the Martinelli et al patent represent successive numerical values or "states", with state No. 10 denoting the completed establishment of a connection between a calling and a called subscriber preparatorily to the exchange of information between these subscribers.